In this paper, we introduce and characterize a subspace of bandlimited signals. The subspace consists of all $Ω$ bandlimited signals such that the non-zero parts of their Fourier transforms are pieces of some $T$ bandlimited signals. The signals in the subspace are called BT-limited signals and the subspace is named as BT-limited signal space. For BT-limited signals, a signal extrapolation with an analytic error estimate exists outside the interval [-T, T] of given signal values with errors. Some new properties about and applying BT-limited signals are also presented.